SciML Comprehensive Non Uniform Grid Support for MethodOfLines

This project aims to deliver comprehensive, end-to-end non-uniform grid support for MethodOfLines.jl. Currently, basic advection schemes lack graceful error handling for ill-posed boundary conditions, and advanced high-order schemes (specifically WENOScheme) completely lack non-uniform method dispatch, leading to fatal compilation errors on irregular domains. The proposed solution utilizes Julia's multiple dispatch to route non-uniform grids to a newly developed, isolated mathematical weight calculator within the WENO module, ensuring zero breaking changes for existing uniform grid users. Key deliverables include refactored basic advection schemes with robust well-posedness validation, a native non-uniform WENO implementation featuring dynamic smoothness indicators and negative weight regularization, rigorous L₂ convergence tests, performance benchmarking, and comprehensive documentation to enable highly precise real-world physics simulations.